Answer:
6,720 ways
Step-by-step explanation:
Since in the problem arrangemnt is being asked this is a problem of permutation.
No . of ways of arranging r things out of n things is given by
P(n,r) = n!/(n-r)!
In the problem given we have to arrange 5 objects from set of 8 objects.
Here n = 8 and p = 5
it can be done in in
P(8,5) = 8!/(8-5)! ways
8!/(8-5)! = 8!/3! = 8*7*6*5*4*3!/3! = 8*7*6*5*4 = 6,720
Thus, number of ways to arrange 5 objects from a set of 8
different objects is P(8,5) = 8!/(8-5)! = 6,720 .
Golden algae are a group of protists whose color is due to carotenoid pigments: yellow and brown. Most have two flagella and all are photosynthetic. A group of students was given a sample of one of these (Dinobryon) that is colonial. Their instructions were to design two or more experiments that could be done with these organisms. The students decide that for one of their experiments, they want to see whether the organisms can photosynthesize. Which of the following is the most appropriate hypothesis for their experiment?
a. If the Dinobryon are kept in the dark, then one-half will be expected to die in 5 days.
b. If the Dinobryon can live without exposure to light for > 5 days, then they must be able to photosynthesize.
c.If the Dinobryon can live > 5 days without added food, then they must be able to photosynthesize.
d.If the Dinobryon are able to photosynthesize, then they should contain photosynthetic pigments
e. If the Dinobryon photosynthesize, then they must need no other minerals or nutrients and will be able to live in distilled water and light alone.
Answer:
Option-D
Step-by-step explanation:
Golden algae are the protists which can photosynthesize and possess flagella. In the given question, a hypothesis has to be proposed which could explain the photosynthesis process in the golden algae process.
A hypothesis is a predicted statement which is based on the previous knowledge and can explain the natural event in. Also, the hypothesis can be tested with the experiments.
The hypothesis shows the possibility of the natural event therefore hypothesis begins with the If the word. In the given question, the statement that if Dinobryon can photosynthesise then they should contain the photosynthetic pigments is considered correct hypothesis which can be tested through the experiments.
Thus, Option-D is the correct answer.
Two points are located along a one dimensional coordinate system. The first point is at 2.1 cm and the second point is at 1.8 cm. What is the distance (in cm) between the two points? [Enter only the numerical value, not the unit cm.]
Answer:
Distance = 0.3
Step-by-step explanation:
We have two point in a line (one dimension).
One point is at 2.1 units and 1.8 units.
The distance between two points can be calculated as the absolute value of the difference between the position of each point.
This can be derived from the distance formula for two dimensions:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\y_1=y_2=0\\\\d=\sqrt{(x_2-x_2)^2}\\\\d=|x_2-x_1|[/tex]
Then, for this case, the distance is:
[tex]d=|1.8-2.1|=|-0.3|=0.3[/tex]
Any help would be greatly appreciated
Answer: 267.9
Step-by-step explanation:
Since we are given the radius, we can plug it into the equation given.
[tex]V=\frac{4}{3} \pi (4)^3[/tex]
[tex]V=\frac{4}{3} \pi (64)[/tex]
[tex]V=267.9[/tex]
There are 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as independent for the purposes of calculations? Are the selections independent or dependent?
Answer:
The selections are dependent.
Yes, they can be treated as independent (less than 5% of the population).
Step-by-step explanation:
Since the selections are made without replacement, each selection affects the outcome of the next selection and, therefore, the selections are dependent.
Although they are dependent, the selections can be treated as independent if the sample size is no more than 5% of the total population. In this case, the sample size is 1235 adults out of a population of 15,958,866 adults. The percentage represented by the sample is:
[tex]P=\frac{12,345}{15,958.866}*100\\ P=0.077\%[/tex]
Thus the selections can be treated as independent for the purposes of calculations.
Which expression is equivalent to
squrt 64a^6
Answer:
[tex]8a^3[/tex]
Step-by-step explanation:
[tex]\sqrt{64a^6}[/tex]
[tex]\sqrt{64} \times \sqrt{a^6}[/tex]
[tex]8 \times \sqrt{a^6}[/tex]
[tex]8 \times a^{6 \times \frac{1}{2} }[/tex]
[tex]8 \times a^{\frac{6}{2} }[/tex]
[tex]8 \times a^3[/tex]
Answer:
[tex]8a^3[/tex]
Step-by-step explanation:
= [tex]\sqrt{64a^6}[/tex]
= [tex]\sqrt{8*8*(a^3)^2}[/tex]
= [tex]8a^3[/tex]
Which of the following lines has a slope of -1/2? my options are x - 2 y = 0 - x + 2 y = 0 x + 2 y = 0
Answer: So x + 2y = 0 is your answer
Step-by-step explanation:
if you look simplify all of these, you will get:
x - 2y = 0
-2y = -x
y = 1/2x No
-x + 2y = 0
2y = x
y = 1/2x No
x + 2y = 0
2y = -x
y = -1/2x Yes!
So x + 2y = 0 is your answer
Answer:So x + 2y = 0 is your answer
Step-by-step explanation:
if you look simplify all of these, you will get:
x - 2y = 0
-2y = -x
y = 1/2x No
-x + 2y = 0
2y = x
y = 1/2x No
x + 2y = 0
2y = -x
y = -1/2x Yes!
So x + 2y = 0 is your answer
Caitlin has cut out a square piece of graph paper that contains a total of 81 blocks.How many blocks are there along one side of the square? Look at the bottom of the page (Number 25)
Answer:
9 squares on each side of the square.
Step-by-step explanation:
[tex]\sqrt{81}=\sqrt{9\times 9}=\sqrt{9^2}=9[/tex]
There are 9 equally sized blocks on one side of square piece of graph paper.
Best Regards!
Which answer shows 2.13786 times 10 Superscript 4 written in standard form?
Answer:
Answer:
21378.6
Step-by-step explanation:
You move the decimal point four places towards the right.
Answer:
21378.6
Step-by-step explanation:
Richard has just been given a 6-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all six questions, find the indicated probabilities. (Round your answers to three decimal places.)
What is the probability that Richard will answer at least half the questions correctly?
Answer:
0.169
Step-by-step explanation:
This is a question on binomial distribution where we only have two outcomes: success or failure
Binomial distribution formula:
P(X= x) = n!/[x!(n-x)!] p^x × q^(n-x)
n is the number of questions in the quiz n = 6
Probability of guessing a correct number = probability of success = p
We told each question has 4 options in which one is correct.
The probability of guessing a correct answer = p= 1/4
p = 0.25
q = 1-p = 1-0.25
q = 0.75
Probability that Richard will answer at least half the questions correctly = P(X≥3)
P(X≥3) = P(X=3) +P(X=4) +P(X=5) +P(X=6)
See attachment for details
P(X≥3) = 0.01318 + 0.0330 + 0.0044 + 0.0002
P(X≥3) = 0.1694
The probability that Richard will answer at least half the questions correctly = 0.169
Using traditional methods, it takes 11.7 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 23 students and observed that they had a mean of 12.1 hours with a standard deviation of 1.4. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
There is no evidence to said that the technique performs differently than the traditional method.
Step-by-step explanation:
First, we need to write the null and alternative hypothesis as:
H0: x = 11.7
H1: x ≠ 11.7
Where x is the population mean for the new method.
Taking into account that the population distribution is approximately normal and the standard deviation of the population is unknown, we can calculated the statistic as:
[tex]t=\frac{x'-x}{\frac{s}{\sqrt{n} } }[/tex]
Where t follows a distribution t-student with n-1 degrees of freedom.
So, replacing x' by the mean of the sample, s by the standard deviation of the sample and n by the size of the sample, we get:
[tex]t=\frac{12.1-11.7}{\frac{1.4}{\sqrt{23} } }=1.37[/tex]
Then, we can find the critical points as:
P(t<t1) = 0.025
P(t<t2) = 0.975
So, with 22 degrees of freedom, the critical point t1 and t2 are equal to -2.07 and 2.07 respectively.
Since 1.37 is between the critical points, we can't reject H0. it means that there is no evidence to said that the technique performs differently than the traditional method.
Which means "a number n increased by 6.2"?
Answer:
n + 6.2
Step-by-step explanation:
Increased here means addition, addition of 6.2 with the number n.
Jimmie invested $57,500 at 9.38% compounded continuously. What will Jimmie's account balance be in 42 years?
Answer:
$6,259,057.84
Step-by-step explanation:
hello,
compounding continuously means that we have to multiply by
[tex]e^{0.0938*t}[/tex]
t is the number of years
so the account balance in 42 years is
[tex]57,500e^{0.0938*42}=6,259,057.84....\\[/tex]
so it gives
$6,259,057.84
hope this helps
Rearrange the following steps in the correct order to locate the last occurrence of the smallest element in a finite list of integers, where the integers in the list are not necessarily distinct.
a. return location
b. min ≔a1 and location ≔1
c. min ≔ai and location≔i
d. procedure last smallest(a1,a2,...,an: integers)
e. If min >= ai then
Answer:
The rearranged steps is as follows:
d. procedure last smallest(a1,a2,...,an: integers)
b. min ≔a1 and location ≔1
e. If min >= ai then
c. min ≔ai and location≔i
a. return location
Step-by-step explanation:
The proper steps to perform the task in the question above is dbeca
Here, the procedure (or function) was defined along with necessary parameters
d. procedure last smallest(a1,a2,...,an: integers)
The smallest number is initialized to the first number on the list and its location is initialized to 1
b. min ≔a1 and location ≔1
The next line is an if conditional statement that checks if the current smallest number is greater than a particular number
e. If min >= ai then
If the above condition is true, the smallest value is assigned to variable min; it's location is also assigned to variable location
c. min ≔ai and location≔i
The last step returns the location of the smallest number
a. return location
will k+10, k+12, k+14 yield consecutive odd integers
Answer:
yes, as long as k is an odd number
Step-by-step explanation:
if k is odd integer
k+10 k +12 K+14 are all odd integer
if k is even integer
k+10 k +12 K+14 are all even integer
hope this helps
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 38443844with a mean life of 997997minutes. If the claim is true, in a sample of 7373batteries, what is the probability that the mean battery life would be greater than 981.7981.7minutes
Answer:
[tex] z = \frac{981.7 -997}{\frac{62}{\sqrt{73}}}= -2.108[/tex]
And we can use the normal standard distribution table or excel and with the complement ruler we got:
[tex] P(z>-2.108) =1- P(z<-2.108) =1-0.0175= 0.9825[/tex]
Step-by-step explanation:
We know the following info given:
[tex]\mu = 997[/tex] represent the true mean
[tex]\sigma = \sqrt{3844}= 62[/tex] represent the population deviation
[tex] n = 73[/tex] represent the sample size selected
Since the sample size is large enough (n>30) we can use the central limit theorem and the sample mean would have the following distribution:
[tex]\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And for this case we want to find this probability:
[tex]P(\bar X >981.7)[/tex]
And we can use the z score formula given by:
[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z = \frac{981.7 -997}{\frac{62}{\sqrt{73}}}= -2.108[/tex]
And we can use the normal standard distribution table or excel and with the complement ruler we got:
[tex] P(z>-2.108) =1- P(z<-2.108) =1-0.0175= 0.9825[/tex]
26
Ping lives at the corner of 3rd Street and 6th Avenue. Ari
lives at the corner of 21st Street and 18th Avenue. There is
a gym į the distance from Ping's home to Ari's home.
24
22
20
n
Ari (21.18)
7
x =
18
(x2 – x) + x3
mi+n
16
Avenue
14
-- ( , Jive - y) +
12
10
Where is the gym?
00
6
Ping (36)
4
2
9th Street and 10th Avenue
12th Street and 12th Avenue
0 14th Street and 12th Avenue
15th Street and 14th Avenue
2
x
4 6 8 10 12 14 16 18 20 22 24 26
Street
Corrected Question
Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym 2/3 the distance from Ping's home to Ari's home. Where is the gym?
9th Street and 10th Avenue 12th Street and 12th Avenue 14th Street and 12th Avenue 15th Street and 14th AvenueAnswer:
(D)15th Street and 14th Avenue
Step-by-step explanation:
Ping's Location: (3rd Street, 6th Avenue)
Ari's Location: (21st Street, 18th Avenue)
The gym is at point P which is [tex]\dfrac{2}{3}[/tex] the distance from Ping's home to Ari's home.
That is, Point P divides the line segment in the ratio 2:1.
We use the section formula:
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
m:n=2:1, [tex](x_1,y_1)=(3,6), (x_2,y_2)=(21,18)[/tex]
[tex]=\left(\dfrac{2*21+1*2}{2+1}, \dfrac{2*18+1*6}{2+1}\right)\\=\left(\dfrac{45}{3}, \dfrac{42}{3}\right)\\=(15,14)[/tex]
The gym is located at 15th Street and 14th Avenue.
Find the area of the smaller sector.
A
6 in
030°
Area = [? ]in?
B
Round your answer to the nearest hundredth.
Answer:
9.42 in²
Step-by-step explanation:
The area of whole circle S=pi*R² , where pi is appr. 3.14, R= 6 in
S= 3.14*6² =113.04 in²
The area of smaller sector is Ssec=S/360*30=113,04/12=9.42 in²
The area of the smaller sector with a central angle of 30 degrees and a radius of 6 inches is 9.42478 square inches.
To find the area of a sector, you can use the formula:
Area of sector = (θ/360) × π × r²
where θ is the central angle in degrees, r is the radius of the sector.
The central angle is 30 degrees and the radius is 6 inches.
Plugging these values into the formula:
Area of sector = (30/360) × π × 6²
= (1/12) × π × 36
= (1/12) × 3.14159 × 36
= 9.42478 square inches
To learn more on Area of sector click:
https://brainly.com/question/29055300
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PLEASE ANSWER, URGENT!!! In a math exam, Zach, Wendy, and Lee have an average score 91. Wendy, Lee and Chen have an average score 89. Zach and Chen have an average score 95. What is Zach's score?
Answer:
98
Step-by-step explanation:
Z as Zach; W as Wendy; L as Lee; C as Chen
We know that average score of Z,W, and L is 91, so:
(z + w + l)/3 = 91
z + w + l = 273
Average score W, L, C = 89, so:
(w + l + c)/3 = 89
w + l + c = 267
We take both:
(z + w + l) – (w + l + c) = 273 – 267
z – c = 6
Average score Z and C = 95
(z + c)/2 = 95
z + c = 190
(z + c) – (z – c) = 184
2c = 184
c = 92
z + c = 190
z + 92 = 190
z = 98
So, Zachs score is 98
6, 9, 15, 24, 36, 51, ?
Answer:
6, 9, 15, 24, 36, 51, 69, 90, 114
Answer:
6, 9, 15, 24, 36, 51, 69, 90, 114 and so on........
How many different ways can the letters of "kissing" be arranged?
Answer:1260
Step-by-step explanation:
Kissing has 7 letters, and there are 2 paris of the same letter.
[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260
Tasha wants to take money out of the ATM for a taxi fare. She wants to do a quick estimate to see if taking $120 out of her bank account will overdraw it. She knows she had $325 in the account this morning when she checked her balance. Today she bought lunch for $19, a dress for $76, a pair of shoes for $53, and a necklace for $23. She also saw a movie with a friend for $12. Rounding each of her expenses to the nearest tens place, estimate how much money Tasha has left in her account before she goes to the ATM. Do not include the $ in your answer.
Answer:145
Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145
Any help would be great
Hey there! :)
Answer:
[tex]-25m^{6}n^{9}[/tex]
Step-by-step explanation:
The product rule means that when multiplying variables with exponents, the exponents must be added together. Therefore:
[tex](-5m^{5}n^{6})(5mn^{3}) =[/tex]
[tex]-25m^{5+1}n^{6+3} =[/tex]
Simplify:
[tex]-25m^{6}n^{9}[/tex]
This is your answer!
The ratio of boys to girls in a group is 2:1. If there are 18 more boys than girls, work out how many girls there are.
Answer:
I think its 18, because if there's 2 boys to 1 girl then if there's 18 girls then there is an equivalent 18 boys to match, plus another 18, which would put the ratio of boy to girl at 2:1
Step-by-step explanation:
Pleasssseeeeee helllllllpppppp
Answer:
Question 2:
A) A and C
B) D and F
Kinda been stuck on this one, someone pls let me know
Answer:
255
Step-by-step explanation:
use calculator
Answer:
255
Step-by-step explanation:
∑ᵢ₌₁⁸ 2ⁱ⁻¹
Using brute force method:
S = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷
S = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
S = 255
Using formula:
S = a₁ (1 − rⁿ) / (1 − r)
S = 1 (1 − 2⁸) / (1 − 2)
S = 255
What is the product ? (7x^2 )(2x^3 +5)(x^2-4x-9)
Answer:
C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Edge 2021
What does 3 represent in the equation y = 3x ? the -intercept the slope yintercept
Answer:
The slope
Step-by-step explanation:
Its equation: y= ax (where a represents the slope)
y =3x
Hope this helps
Good Luck
1/5 as a percent rounded to the nearest hundredth
Answer:
1/5 as a percent is 20%
Step-by-step explanation:
Answer: 20%
Step-by-step explanation: Let's turn it into a decimal by dividing!
1 ÷ 5 = 0.2
0.2 x 100 = 20 = 20%
I hope this helps!
Please answer this correctly
Answer:
There are 10 teams.
Step-by-step explanation:
Given that the question wants at least 48 swimmers so any numbers above 47 are counted.
In this diagram, there are 10 teams consisting 48 swimmers and above, 48, 52, 53, 63, 76, 79, 82, 84, 85 and 86.
Answer:
10 teams have 48 or more swimmers.
Step-by-step explanation:
If we look at stem 4 there is one team with 48 members.
So counting from there we have:
1 + 2 + 1 + 2 + 4
= 10 teams.
Help me please thank u
Answer:
4+3n
Step-by-step explanation:
We get the formula 4+3n because the pattern is +3 each term starting with the first term as 7. Since the first term is 7, we get 4+3n.
